Wang tiles for image and texture generation l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 34

Wang Tiles for Image and Texture Generation PowerPoint PPT Presentation


  • 336 Views
  • Uploaded on
  • Presentation posted in: General

Wang Tiles for Image and Texture Generation. Michael Cohen Microsoft Research Jonathan Shade University of Washington and WildTangent Stefan Hiller University of Constance Oliver Deussen University of Constance. Wang Tiles. Rules Tilings are assembled by matching like edges

Download Presentation

Wang Tiles for Image and Texture Generation

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Wang tiles for image and texture generation l.jpg

Wang Tiles for Image and Texture Generation

Michael CohenMicrosoft Research

Jonathan ShadeUniversity of Washington

and WildTangent

Stefan HillerUniversity of Constance

Oliver DeussenUniversity of Constance


Wang tiles l.jpg

Wang Tiles

  • Rules

    • Tilings are assembled by matching like edges

    • Tiles cannot be rotated

  • In 1961 Wang asserted that no aperiodic set of tiles exists, i.e., a set that

    • COULD tile the plane

    • could NOT tile it periodically

  • He was wrong, but still got to keep his name on them

  • Aperiodic sets can be used to

    • Simulate Turing machines

    • Act as life forms in science fiction (“Wang’s Carpets” by Greg Egan)


Wang tiles not new to cg l.jpg

Wang Tiles – not new to CG

  • Jos Stam

    • Showed the use of aperiodic tile sets for texture assembly


Wang tiles not new to cg4 l.jpg

Wang Tiles – not new to CG

  • Jos Stam

    • Showed the use of aperiodic tile sets for texture assembly

  • Neyret and Cani

    • Used triangular tiles with coded edges to assure continuous texture


Wang tiles5 l.jpg

Wang Tiles

Wang Tiles

Mirrored


Wang tiles6 l.jpg

Wang Tiles


Wang tiles7 l.jpg

Wang Tiles

  • We introduce non-periodic tilings

    • set can trivially tile the plane periodically

    • simple stochastic algorithm → non-periodic

non-periodic

aperiodic


Wang tiles8 l.jpg

Wang Tiles

  • 2 colors = 8 tiles

  • 3 colors = 18 tiles

  • C colors ?

2 x C2


Why wang tiles l.jpg

Why Wang Tiles?

  • Once you fill a set of Wang Tiles with stuff

  • You can create as much of that stuff as you want for almost free.

Free stuff!

Free stuff!

Demo


Wang tiles for texture synthesis l.jpg

Wang Tiles for Texture Synthesis


Wang tiles for texture synthesis11 l.jpg

Wang Tiles for Texture Synthesis


Wang tiles for texture synthesis12 l.jpg

Wang Tiles for Texture Synthesis


Wang tiles for texture synthesis13 l.jpg

Wang Tiles for Texture Synthesis


Wang tiles for texture synthesis14 l.jpg

Wang Tiles for Texture Synthesis


Wang tiles for texture synthesis15 l.jpg

Wang Tiles for Texture Synthesis

Demo


Wang tiles for texture synthesis16 l.jpg

Wang Tiles for Texture Synthesis


Wang tiles the corner problem l.jpg

?

Wang Tiles: the corner problem


Wang tiles the corner problem18 l.jpg

Wang Tiles: the corner problem


Wang tiles the corner problem19 l.jpg

Wang Tiles: the corner problem

A better solution? Lefebvre and Neyret, I3D 2003


Wang tiles for distributions l.jpg

Wang Tiles for Distributions

Poisson Disc Distributions


Wang tiles for distributions21 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions22 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions23 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions24 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions25 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions26 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions27 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions28 l.jpg

Wang Tiles for Distributions


Wang tiles for distributions29 l.jpg

Wang Tiles for Distributions


3d wang tiles l.jpg

3D Wang Tiles

  • Volumetric tiles filled with 3D “texture”

  • In this example, 2.5D

  • Layered Depth Image samples


3d wang tiles31 l.jpg

3D Wang Tiles

  • Hierarchical

  • View Dependent


3d wang tiles32 l.jpg

3D Wang Tiles


Wang tiles33 l.jpg

Wang Tiles

  • Simple stochastic assembly: non-periodic

  • Texture synthesis

  • Distribution synthesis

  • The corner problem

  • Some 3D applications

Free stuff!

Free stuff!


Wang tiles34 l.jpg

Wang Tiles

T

H

A

N

K

Y

O

U

Don Mitchell

Alex Colburn

Reviewers


  • Login